What is the general solution for (tan(θ)cos(θ))/(csc(θ))=sin(θ) ?

The general solution for (tan(θ)cos(θ))/(csc(θ))=sin(θ) is No Solution for θ\in\mathbb{R}

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(tan(θ)cos(θ))/(csc(θ))=sin(θ)

\frac{tan ( θ ) cos ( θ )}{csc ( θ )} = sin (θ)

No Solution for θ \in R

Solution steps

\frac{tan ( θ ) cos ( θ )}{csc ( θ )} = sin (θ)

Subtract

sin (θ)

from both sides

\frac{tan ( θ ) cos ( θ )}{csc ( θ )} - sin (θ) = 0

Simplify

\frac{tan ( θ ) cos ( θ )}{csc ( θ )} - sin (θ) : \frac{tan ( θ ) cos ( θ ) - sin ( θ ) csc ( θ )}{csc ( θ )}

\frac{tan ( θ ) cos ( θ ) - sin ( θ ) csc ( θ )}{csc ( θ )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

tan (θ) cos (θ) - sin (θ) csc (θ) = 0

Rewrite using trig identities

- 1 + sin (θ) = 0

Move

1

to the right side

sin (θ) = 1

General solutions for

sin (θ) = 1

θ = \frac{π}{2} + 2 πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn

No Solution for θ \in R

sin (θ) = \frac{44}{12}

cos (A) = \frac{2 ^{2} + 2.2 4 ^{2} - 2.2 4 ^{2}}{2 ( 2 ) ( 2.24 )}

cos (θ) = - \frac{3}{5}, θ, 3

sin (3 x) = 0.5

cos^{2} (x) - 5 sin (x) + 5 = 0

What is the general solution for (tan(θ)cos(θ))/(csc(θ))=sin(θ) ?
The general solution for (tan(θ)cos(θ))/(csc(θ))=sin(θ) is No Solution for θ\in\mathbb{R}